Network Flows: Theory, Algorithms, and ApplicationsA comprehensive introduction to network flows that brings together the classic and the contemporary aspects of the field, and provides an integrative view of theory, algorithms, and applications.
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Page 67
... objective func- tion value proportional to the difference between the objective values of the current and optimal solutions . Let H be the difference between the maximum and minimum objective function values of an optimization problem ...
... objective func- tion value proportional to the difference between the objective values of the current and optimal solutions . Let H be the difference between the maximum and minimum objective function values of an optimization problem ...
Page 333
... objective function ( 9.25a ) of the relaxed problem in another way . Notice ... value between 0 and u . The resulting solution is a pseudoflow for the ... objective function value of the minimum cost flow problem . As shown by the next ...
... objective function ( 9.25a ) of the relaxed problem in another way . Notice ... value between 0 and u . The resulting solution is a pseudoflow for the ... objective function value of the minimum cost flow problem . As shown by the next ...
Page 603
... objective function value is z ( x ) = 100. The number of potential integer solutions in F1 is still 2'- ' , so it will be prohibitively expensive to enumerate all these possibilities , except when J is small . Rather than attempt to ...
... objective function value is z ( x ) = 100. The number of potential integer solutions in F1 is still 2'- ' , so it will be prohibitively expensive to enumerate all these possibilities , except when J is small . Rather than attempt to ...
Contents
INTRODUCTION | 1 |
PATHS TREES AND CYCLES | 23 |
ALGORITHM DESIGN AND ANALYSIS | 53 |
Copyright | |
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adjacency list Application arc costs arc flows arc lengths augmenting path augmenting path algorithm bipartite capacity scaling algorithm commodity constraints cost flow problem define denote Dijkstra's algorithm directed path discussion distance label example Exercise feasible flow feasible solution Fibonacci heap flow algorithms formulation implementation integer iteration label-correcting algorithm Lagrangian multiplier Lagrangian relaxation Lemma linear programming lower bound matching matrix maximum flow problem minimum cost flow minimum spanning tree multicommodity flow problem N₁ negative cycle network contains network flow problem network G network simplex algorithm node potentials nonnegative NP-complete O(nm objective function value operation optimal solution optimality conditions path from node polynomial preflow-push algorithm reduced cost residual network s-t cut satisfies scaling phase Section shortest path distances shortest path problem Show shown in Figure simplex method source node Suppose Theorem undirected units of flow upper bound variables zero